To increase the region of validity of this equation, the logarithm of the
gamma function that appears on its left-hand side has been changed to
, where is the general logarithm.
Originally was used, where
is the principal branch of the logarithm.
For exact values of to and 40S values of to ,
see Char (1980). Also see Cuyt et al. (2008, pp. 223–228),
Jones and Thron (1980, pp. 348–350), Lorentzen and Waadeland (1992, pp. 221–224),
and Jones and Van Assche (1998).